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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Udon Thani

about 6 hours ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

about 6 hours ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

about 6 hours ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

about 17 hours ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

a day ago
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

a day ago
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

November 6, 2019 at 12:06am

#969085

Oy, This Dreck Again

PROMPT November 6th

I have another link for you all today:

http://www.wmfc.org/uploads/GenerationalDifferencesChart.pdf

What parts of the chart did you find to be accurate and which did you find issue with? Anything you related strongly to? Is a chart like this useful, or does it rely too heavily on stereotypes?

I've said this before and I haven't run into anything that has changed my opinion: "generations" are utter bullshit; people are born, live and die on a continuum; and attempts to pigeonhole us are about as useful and accurate as star charts and Facebook quizzes.

Also, as Barack Obama (misspelled on the chart) is listed as a GenXer when by its own reckoning he's a Boomer, having been born (IN THE US FOR FUCK'S SAKE) in 1961. Given that simple error (compounded by the typo), I can't trust anything the chart says. And further yet, by my calculations it's a good 11-12 years out of date now.

And what the hell is it with the two date ranges for Millennials? Can't that generation do anything right? (KIDDING I'M KIDDING JEEZE)

Again, I've run through this argument before, but for newcomers: I was born in 1966. That would put me in GenX, along with people born (per the chart) in 1980. So they'd lump me in with someone from 1980, 14 years distant, but not from 1964, 2 years separated? How about twins born on the cusp of 1964-65? Theoretically, one could be a Boomer and his or her little sibling (by all of three minutes) could be an Xer. That could make Thanksgivings way fun as the older sibling could throw "kids these days" shade at the younger one.

It's really remarkable how much work has gone into the preparation of this nonsense chart, without even the fun math involved in astrology, or the years of college needed to come up with a Myers-Briggs analysis.

The whole "generations" thing was developed, I'm pretty sure, as a tool for marketers as a way to target people for manipulation. This is seen nakedly in the stuff at the very bottom of the chart, which admittedly I skimmed down to.

I'm not saying everything in it is wrong, of course - after all, Xers are "skeptical" and "cynical." Hey, spot on there. Stopped clock and all that.

So of course I tried to track down where the pdf came from. The webpage corresponding to the domain in the pdf's URL (try telling THAT to someone from 1965) is the West Midland Family Center, out of Michigan - hence, one supposes, the focus on the various cohorts' work ethics and "fundraising tips."

But that gives me the opportunity to point out a rule that has never led me astray in all the years I've followed it. To wit:

Never trust an organization with the word "Family" in the name.

Inevitably, they are run by people who are appalled at the idea that someone, somewhere, who is not a child, is having fun, and will work very, very hard to stop that nonsense immediately.

Now, I don't know... I haven't clicked around that particular organization's website very much. Could be they're an exception. I wouldn't bet the farm on it, though. (I actually do own a farm, by the way. That's not just an expression for me.)

6 Like • Comment • View 5 comments

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